Lockable drawer containers, such as filing cabinets and tool chests and cabinets, feature a variety of locking mechanisms and features. Many lockable chests include a keyed lock cylinder that actuates a locking mechanism that locks the drawers in a closed position. Once the chest is locked, it is difficult or impossible to close and secure a drawer that was open at the time the locking mechanism was actuated. If a drawer is inadvertently or otherwise left open during locking, it is thus necessary for a proper key to be used to unlock the chest, close the drawer, and re-lock the chest.